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Cyclic Vectors in Banach Spaces of Analytic Functions

Chapter
Part of the NATO ASI series book series (ASIC, volume 153)

Abstract

In these three lectures we consider Banach spaces of analytic functions on plane domains. If the space admits the operator of multiplication by z, then it is of interest to describe the cyclic vectors for this operator, that is, those functions in the space with the property that the polynomial multiples of the function are dense. A necessary condition is that the function have no zeros; in general it is difficult to give necessary and sufficient conditions.

Keywords

Banach Space Analytic Function Invariant Subspace Bergman Space Blaschke Product 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© D. Reidel Publishing Company 1985

Authors and Affiliations

  1. 1.Department of MathematicsThe University of MichiganAnn ArborUSA

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